Root Locus Design
Concepts
1
Control System Including a Delay
2
First-Order Time Lag Plus Dead Time
3
Root Locus without Delay (T = 0;
Gp(S) = 1/S); H(S) = 1
4
Root Locus with Delay (T = 1; K varies)
• >> n=[-1 2] ;d=[1 2 0];
• >> r=rlocus(n,d);
• >> plot(r,'-');
• >>v=[-3 10 -3 3]; >>axis(v);
• >>axis('square')
• >> grid
5
Root Locus with Delay (K = 2; 1/T varies)
6
Conclusion
• As a system is driven at larger gains (faster response), the value of the
delay must be smaller for stability.
7
System to be Compensated
8
Proportional Compensated R-L
[Gc(S)Gp(S) = K/(S + 2)2
9
Step Response for T(S) = K/(S2 + 2S + K + 1) and K = 1
10
Integral-Compensated Root Locus
11
Step Response with K = 1
12
Proportional–Plus-Derivative compensated R-L
13
Step Response for T(S) = K(S + 2)/[S2 + (2 + K)S + 2K]
and K = 1
14
Light-Source Tracking System
15
Block Diagram
16
Root Locus
17
Typical Responses to Step
18
Block Diagram with Position and Rate
Feedback
19
Signal Flow Graph
20
Unit Step Response with K = 250;
K’ = 0.08
21